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JEE Main 2023 January 25, Shift 2 Question Paper with Solutions

All 90 questions from the JEE Main 2023 (January 25, Shift 2) shift — Physics (30), Chemistry (30) and Mathematics (30) — each with the correct answer (answer key) and a step-by-step solution. Read it free online, or attempt the full paper as a timed mock test.

Physics30 questions

Q1Single correctGravitation
Every planet revolves around the sun in an elliptical orbit:
A. The force acting on a planet is inversely proportional to square of distance from sun.
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun.
C. The Centripetal force acting on the planet is directed away from the sun.
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit.
Choose the correct answer from the options given below:
(A)
(B)
(C)
(D)
Q2Single correctThermodynamics
Choose the correct answer from the options given below:
List IList II
A.. Isothermal ProcessI.. Work done by the gas decreases internal energy
B.. Adiabatic ProcessII.. No change in internal energy
C.. Isochoric ProcessIII.. The heat absorbed goes partly to increase internal energy and partly to do work
D.. Isobaric ProcessIV.. No work is done on or by the gas
(A)
(B)
(C)
(D)
Q3Single correctElectrostatics
A point charge of is placed at the origin. At what location on the X-axis should a point charge of be placed so that the net electric field is zero at cm on the X-axis?
(A)
(B)
(C)
(D)
Q4Single correctThermal Properties of Matter
The graph between two temperature scales P and Q is shown in the figure. Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two scales is given by
Graph of Temperature (deg P) vs Temperature (deg Q): a straight line, with delta_tP=150 deg (vertical) and delta_tQ=100 deg (horizontal) marked.
(A)
(B)
(C)
(D)
Q5Single correctDual Nature of Radiation and Matter
Given below are two statements:
Statement I: Stopping potential in photoelectric effect does not depend on the power of the light source.
Statement II: For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light.
In the light of above statements, choose the most appropriate answer from the options given below:
(A)
(B)
(C)
(D)
Q6Single correctRay Optics
The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are: -
A. Real
B. Erect
C. Smaller in size than object
D. Laterally inverted
Choose the most appropriate answer from the options given below:
(A)
(B)
(C)
(D)
Q7Single correctProjectile Motion
Two objects are projected with same velocity 'u' however at different angles and with the horizontal. If , the ratio of horizontal range of the first object to the 2nd object will be:
(A)
(B)
(C)
(D)
Q8Single correctAtmospheric Physics
Choose the correct answer from the options given below:
List IList II
A.. TroposphereI.. Approximate 65-75 km over Earth's surface
B.. E-Part of StratosphereII.. Approximate 300 km over Earth's surface
C.. -Part of ThermosphereIII.. Approximate 10 km over Earth's surface
D.. D-Part of StratosphereIV.. Approximate 100 km over Earth's surface
(A)
(B)
(C)
(D)
Q9Single correctAtoms
The energy levels of an atom is shown in figure.
Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm?
Given ( Js)
Atomic energy-level diagram: four levels at 0.0, -2.2, -5.2, -10.0 eV with downward transitions A,B,C,D.
(A)
(B)
(C)
(D)
Q10Single correctMoving Charges and Magnetism
For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passed through it. If the torsional constant of suspension wire is N m , the magnetic field is 0.01 T and the number of turns in the coil is 200, the area of each turn (in ) is :
(A)
(B)
(C)
(D)
Q11Single correctOscillations
A particle executes simple harmonic motion between and . If time taken by particle to go from to is 2 s; then time taken by particle in going from to A is
(A)
(B)
(C)
(D)
Q12Single correctElectromagnetic Induction
A wire of length 1 m moving with velocity 8 m/s at right angles to a magnetic field of 2 T. The magnitude of induced emf, between the ends of wire will be________.
(A)
(B)
(C)
(D)
Q13Single correctMotion in a Straight Line
The distance travelled by a particle is related to time t as . The velocity of the particle at s is.
(A)
(B)
(C)
(D)
Q14Single correctGravitation
A body of mass is taken from earth surface to the height h equal to twice the radius of earth , the increase in potential energy will be:
( acceleration due to gravity on the surface of Earth)
(A)
(B)
(C)
(D)
Q15Single correctUnits and Measurements
Choose the correct answer from the options given below.
List IList II
A.. Young's Modulus (Y)I..
B.. Co-efficient of Viscosity ()II..
C.. Planck's Constant (h)III..
D.. Work Function ()IV..
(A)
(B)
(C)
(D)
Q16Single correctElectromagnetic Waves
Choose the correct answer from the options given below :
List IList II
A.. Gauss's Law in ElectrostaticsI..
B.. Faraday's LawII..
C.. Gauss's Law in MagnetismIII..
D.. Ampere-Maxwell LawIV..
(A)
(B)
(C)
(D)
Q17Single correctKinetic Theory of Gases
According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :
(A)
(B)
(C)
(D)
Q18Single correctLaws of Motion
Consider a block kept on an inclined plane (inclined at ) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane is equal to
A hatched square block resting on a 45-degree inclined plane (right triangle with dashed horizontal base).
(A)
(B)
(C)
(D)
Q19Single correctSemiconductor Electronics
Statement I : When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic it becomes N-type semiconductor such that P-type has excess holes and N-type has excess electrons.
Statement II : When such P-type and N-type semiconductors, are fused to make a junction, a current will automatically flow which can be detected with an externally connected ammeter.
In the light of above statements, choose the most\ appropriate answer from the options given below.
(A)
(B)
(C)
(D)
Q20Single correctCurrent Electricity
The resistance of a wire is . It's new resistance in ohm if stretched to 5 times of it's original length will be
(A)
(B)
(C)
(D)
Q21NumericalMagnetic Effects of Current and Magnetism
Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P is _______ T.
Two parallel wires end-on: 15 A (left) and 8 A (right), 7 cm apart, with 7/sqrt2 cm slant distances to a point P at right angle.
Q22NumericalRotational Motion
If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about a tangent will be . Then the value of x is _______
A solid sphere of mass m=5 kg rotating about a vertical axis tangent to its right edge.
Q23NumericalRay Optics and Optical Instruments
An object is placed on the principal axis of convex lens of focal length 10 cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm. The image produced by the plane mirror is 5 cm inside the mirror. The distance of the object from the lens is _______ cm.
Optical axis with object O on the left, a convex lens L at centre, and a plane mirror M on the right, 20 cm from the lens.
Q24NumericalCurrent Electricity
Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of . Cell 2 has emf of 6 V and internal resistance of . An external resistor R of is connected across A and B. The current flowing through R will be _______ A.
Two cells in parallel between A and B: Cell 1 (12 V, 3 ohm) and Cell 2 (6 V, 6 ohm).
Q25NumericalElectrostatic Potential and Capacitance
A capacitor has capacitance when it's parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness is inserted between the plates. Capacitance of the capacitor in the presence of slab will be _______ .
Parallel-plate capacitor of separation d with a dielectric slab of thickness d/2 partially inserted.
Q26NumericalOscillations and Waves
A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency of the observer will be (given speed of sound ) Hz.
Q27NumericalAtoms and Nuclei
A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3:2. The ratio of their nuclear sizes will be . The value of 'x' is _______
Q28NumericalLaws of Motion
A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision is _______ m.
Q29NumericalAlternating Current
A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance , an inductor of inductive reactance , and a capacitor of capacitive reactance . The power factor of circuit is . The value of X is :
Series LCR loop: R=80 ohm, X_L=70 ohm, X_C=130 ohm, with an AC source.
Q30NumericalMechanical Properties of Fluids
A spherical drop of liquid splits into 1000 identical spherical drops. If is the surface energy of the original drop and is the surface energy of the resulting drops, the (ignoring evaporation), . Then value of x is _______ :

Chemistry30 questions

Q31Single correctClassification of Elements and Periodicity in Properties
Which of the following represents the correct order of metallic character of the given elements?
(A)
(B)
(C)
(D)
Q32Single correctAmines
Choose the correct answer from the options given below.
LIST-I (Amines)LIST-II ()
A.. AnilineI.. 3.25
B.. EthanamineII.. 3.00
C.. N-EthylethanamineIII.. 9.38
D.. N, N-DiethylethanamineIV.. 3.29
(A)
(B)
(C)
(D)
Q33Single correctp-Block Elements
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Carbon forms two important oxides – CO and C. CO is neutral whereas C is acidic in nature.
Reason R : C can combine with water in a limited way to form carbonic acid, while CO is sparingly soluble in water.
In the light of the above statements, choose the most appropriate answer from the options given below.
(A)
(B)
(C)
(D)
Q34Single correctChemical Bonding and Molecular Structure
Statement I : Dipole moment is a vector quantity and by convention it is depicted by a small arrow with tail on the negative centre and head pointing towards the positive centre.
Statement II : The crossed arrow of the dipole moment symbolized the direction of the shift of charges in the molecules.
In the light of the above statements, choose the most appropriate answer from the options given below.
(A)
(B)
(C)
(D)
Q35Single corrects-Block Elements
Which one among the following metals is the weakest reducing agent?
(A)
(B)
(C)
(D)
Q36Single correctAlcohols, Phenols and Ethers
Find out the major product from the following reaction.
(The reactant is cyclohexanol bearing a methyl substituent; reagent: (Concentrated), .)
Q36 reaction scheme
(A)
(B)
(C)
(D)
Q37Single correctEnvironmental Chemistry
A. Ammonium salts produce haze in atmosphere.
B. Ozone gets produced when atmospheric oxygen reacts with chlorine radicals.
C. Polychlorinated biphenyls act as cleansing solvents.
D. 'Blue baby' syndrome occurs due to the presence of excess of sulphate ions in water.
Choose the correct answer from the options given below.
(A)
(B)
(C)
(D)
Q38Single correctGeneral Principles and Processes of Isolation / Qualitative Analysis
A chloride salt solution acidified with dil.HN gives a curdy white precipitate, [A], on addition of AgN. [A] on treatment with NOH gives a clear solution, B. A and B are respectively
(A)
(B)
(C)
(D)
Q39Single correctPolymers
Choose the correct answer from the options given below.
LIST-I (Name of Polymer)LIST-II (Uses)
A.. GlyptalI.. Flexible pipes
B.. NeopreneII.. Synthetic wool
C.. AcrilanIII.. Paints and Lacquers
D.. LDPIV.. Gaskets
(A)
(B)
(C)
(D)
Q40Single correctOrganic Chemistry — Some Basic Principles
Choose the correct answer from the options given below.
LIST-I (Isomeric pairs)LIST-II (Type of isomers)
A.. Propanamine and N-MethylethanamineI.. Metamers
B.. Hexan-2-one and Hexan-3-oneII.. Positional isomers
C.. Ethanamide and HydroxyethanimineIII.. Functional isomers
D.. o-nitrophenol and p-nitrophenolIV.. Tautomers
(A)
(B)
(C)
(D)
Q41Single correctRedox Reactions / d- and f-Block Elements
Potassium dichromate acts as a strong oxidizing agent in acidic solution. During this process, the oxidation state changes from
(A)
(B)
(C)
(D)
Q42Single correctPhenols / Chemistry in Everyday Life
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Butylated hydroxy anisole when added to butter increases its shelf life.
Reason R : Butylated hydroxy anisole is more reactive towards oxygen than food.
In the light of the above statements, choose the most appropriate answer from the options given below
(A)
(B)
(C)
(D)
Q43Single correctEquilibrium
When the hydrogen ion concentration [H] changes by a factor of 1000, the value of pH of the solution ___________
(A)
(B)
(C)
(D)
Q44Single correctHaloalkanes and Haloarenes
The isomeric deuterated bromide with molecular formula DBr having two chiral carbon atoms is
(A)
(B)
(C)
(D)
Q45Single correctCoordination Compounds
Choose the correct answer from the options given below.
LIST I (Coordination entity)LIST II (Wavelength of light absorbed in nm)
A.. I.. 310
B.. II.. 475
C.. III.. 535
D.. IV.. 600
(A)
(B)
(C)
(D)
Q46Single correctAldehydes, Ketones and Carboxylic Acids
'A' in the given reaction is
Q46 reaction scheme
(A)
(B)
(C)
(D)
Q47Single corrects-Block Elements
Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The alkali metals and their salts impart characteristic colour to reducing flame.
Reason R: Alkali metals can be detected using flame tests.
In the light of the above statements, choose the most appropriate answer from the options given below.
(A)
(B)
(C)
(D)
Q48Single correctHydrogen
Choose the correct answer from the options given below:
LIST ILIST II
A.. Cobalt catalystI.. production
B.. SyngasII.. Water gas production
C.. Nickel catalystIII.. Coal gasification
D.. Brine solutionIV.. Methanol production
(A)
(B)
(C)
(D)
Q49Single correctGeneral Principles and Processes of Isolation of Elements
Given below are two statements:
Statement I : In froth floatation method a rotating paddle agitates the mixture to drive air out of it.
Statement II : Iron pyrites are generally avoided for extraction of iron due to environmental reasons.
In the light of the above statements, choose the correct answer from the options given below:
(A)
(B)
(C)
(D)
Q50Single correctSolutions
What is the mass ratio of ethylene glycol molar mass = 62 g/mol) required for making 500 g of 0.25 molal aqueous solution and 250 mL of 0.25 molal aqueous solution?
(A)
(B)
(C)
(D)
Q51NumericalChemical Kinetics
A first order reaction has the rate constant, . The number of correct statement/s from the following is/are____________
Given:
A. Reaction completes in 1000 s.
B. The reaction has a half-life of 500 s.
C. The time required for 10% completion is 25 times the time required for 90% completion.
D. The degree of dissociation is equal to
E. The rate and the rate constant have the same unit.
Q52NumericalSurface Chemistry
The number of incorrect statement/s from the following is/are____________
A. Water vapours are absorbed by anhydrous calcium chloride.
B. There is a decrease in surface energy during adsorption.
C. As the adsorption proceeds, becomes more and more negative.
D. Adsorption is accompanied by decrease in entropy of the system.
Q53NumericalSome Basic Concepts of Chemistry
Number of hydrogen atoms per molecule of a hydrocarbon A having 85.8% carbon is __________.
(Given: Molar mass of A = 84 g mo)
Q54NumericalAtomic Structure
The number of atomic orbitals having electron density along the axis is __________.
Q55NumericalAlcohols, Phenols and Ethers; Aldehydes and Ketones
Number of compounds giving (i) red colouration with ceric ammonium nitrate and also (ii) positive iodoform test from the following is _____
Eight candidate organic structures (acetophenone, alcohols, aldehyde, ether, etc.) to be classified.
Q56NumericalSolutions
The number of pairs of the solutions having the same value of the osmotic pressure from the following is _________.
(Assume 100% ionization)
A. 0.500 M (aq) and 0.25 M KBr (aq)
B. 0.100 M (aq) and 0.100 M (aq)
C. 0.05 M (aq) and 0.25 M NaCl (aq)
D. 0.15 M NaCl (aq) and 0.1 M (aq)
E. 0.02 M KCl. (aq) and 0.05 M KCl (aq)
Q57NumericalThermodynamics
28.0 L of is produced on complete combustion of 16.8 L gaseous mixture of ethene and methane at and 1 atm. Heat evolved during the combustion process is ____________ kJ.
Given:
Q58NumericalElectrochemistry

The for the given cell is 0.1115 V at 298 K when

The value of a is _________
Given:
Q59NumericalCoordination Compounds
Total number of moles of AgCl precipitated on addition of excess of to one mole each of the following complexes , , and is __________
Q60NumericalStates of Matter
Based on the given figure, the number of correct statement/s is/are _________
A. Surface tension is the outcome of equal attractive and repulsive forces acting on the liquid molecule in bulk.
B. Surface tension is due to uneven force acting on the molecules present on the surface.
C. The molecule in the bulk can never come to the liquid surface.
D. The molecules on the surface are responsible for vapour pressure if the system is a closed system.
A beaker of liquid showing a surface molecule with net inward force vs a balanced bulk molecule (surface tension).

Mathematics30 questions

Q61Single correctMatrices and Determinants
Let and , where .
If , then the inverse of the matrix is
(A)
(B)
(C)
(D)
Q62Single correctVector Algebra
Let , and . Then is equal to
(A)
(B)
(C)
(D)
Q63Single correctMathematical Reasoning
Let be such that is a tautology. Then
(A)
(B)
(C)
(D)
Q64Single correctCoordinate Geometry
The equations of two sides of a variable triangle are and , and its third side is a tangent to the parabola . The locus of its circumcentre is
(A)
(B)
(C)
(D)
Q65Single correctThree Dimensional Geometry
The shortest distance between the lines and is
(A)
(B)
(C)
(D)
Q66Single correctLimits, Continuity and Differentiability
If the function is continuous at , then is equal to
(A)
(B)
(C)
(D)
Q67Single correctVector Algebra
If the four points, whose position vectors are , , and are coplanar, then is equal to
(A)
(B)
(C)
(D)
Q68Single correctCoordinate Geometry
Let T and C respectively be the transverse and conjugate axes of the hyperbola . Then the area of the region above the parabola , below the transverse axis T and on the right of the conjugate axis C is :
(A)
(B)
(C)
(D)
Q69Single correctPermutations and Combinations
The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition, is
(A)
(B)
(C)
(D)
Q70Single correctDifferential Equations
Let be a solution of the differential equation where, , and . Then
(A)
(B)
(C)
(D)
Q71Single correctPermutations and Combinations
is equal to
(A)
(B)
(C)
(D)
Q72Single correctMatrices and Determinants
Let A,B,C be matrices such that A is symmetric and B and C are skew-symmetric. Consider the statements
(S1) is symmetric
(S2) is symmetric
Then,
(A)
(B)
(C)
(D)
Q73Single correctSequences and Series
Let and , . Then the sum of all the positive integer divisors of is
(A)
(B)
(C)
(D)
Q74Single correctRelations and Functions
The number of functions satisfying is
(A)
(B)
(C)
(D)
Q75Single correctApplications of Derivatives
Let the function have a maxima for some value of and a minima for some value of . Then, the set of all values of p is
(A)
(B)
(C)
(D)
Q76Single correctIntegral Calculus
The integral is equal to
(A)
(B)
(C)
(D)
Q77Single correctSets, Relations and Functions
Let be a function defined by , for some m, such that the range of f is . Then the value of m is __________
(A)
(B)
(C)
(D)
Q78Single correctProbability
Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that are in geometric progression be . Then the value of k is
(A)
(B)
(C)
(D)
Q79Single correctComplex Numbers and Quadratic Equations
Let z be a complex number such that . Then z lies on the circle of radius and centre
(A)
(B)
(C)
(D)
Q80Single correctThree Dimensional Geometry
The foot of perpendicular of the point on the line is . Then, which of the following is NOT correct?
(A)
(B)
(C)
(D)
Q81NumericalComplex Numbers and Quadratic Equations
Let and let be the roots of the equation . If , then the product of all possible values of a is __________
Q82NumericalSequences and Series
For the two positive number a,b, if a,b and are in a geometric progression, while and are in an arithmetic progression, then is equal to __________
Q83NumericalCo-ordinate Geometry
Points and lie on a circle C with PR as its diameter. The tangents to C at the points Q and R intersect at the point S. If S lies on the line , then K is equal to
Q84NumericalThree Dimensional Geometry
If the shortest distance between the line joining the points and , and the line is , then is equal to __________
Q85NumericalPermutations and Combinations
Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer 5 fruits to Anil is __________
Q86NumericalProbability
25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non-smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is . Then the value of k is __________
Q87NumericalCo-ordinate Geometry
A triangle is formed by X-axis and the line . Then the number of points P(a,b), which lie strictly inside the triangle, where a is integer and b is a multiple of a, is __________
Q88NumericalNumber Theory
The remainder when is divided by is __________
Q89NumericalTrigonometry
If m and n respectively are the numbers of positive and negative values of in the interval that satisfy the equation , then mn is equal to __________
Q90NumericalIntegral Calculus
If , where m and n are coprime natural numbers, then is equal to __________

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The JEE Main 2023 January 25, Shift 2 paper has 90 questions — Physics (30), Chemistry (30) and Mathematics (30). Every question is on this page with its correct answer and a step-by-step solution.

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JEE Main awards +4 marks for each correct answer and −1 for a wrong answer, with 0 for questions left unattempted. The paper covers Physics, Chemistry and Mathematics.

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